Answer

Verified

429.6k+ views

**Hint:**Here, we need to find the surface area of the resulting cuboid. First, we will find the length of the side of the two cubes. Then, we will find the dimensions of the resulting cuboid when the two cubes are joined end to end. We will then use the formula for total surface area of a cuboid and simplify it to find the required answer.

**Formula used:**We will use the following formula to solve the questions:

The volume of a cube is given by the formula \[V = {a^3}\], where \[a\] is the length of the side of the cube.

The total surface area of a cuboid is given by the formula \[2\left( {lb + bh + lh} \right)\], where \[l\] is the length, \[b\] is the breadth, and \[h\] is the height.

**Complete step-by-step answer:**First, we will find the length of the side of the cubes using the formula for volume of a cube.

The volume of a cube is given by the formula \[V = {a^3}\], where \[a\] is the length of the side of the cube.

Substituting \[V = 64{\rm{ c}}{{\rm{m}}^3}\] in the formula, we get

\[ \Rightarrow 64 = {a^3}\]

Taking cube root of both sides, we get

\[\begin{array}{l} \Rightarrow \sqrt[3]{{64}} = \sqrt[3]{{{a^3}}}\\ \Rightarrow a = 4{\rm{ cm}}\end{array}\]

Therefore, the length of the side of the cube is 4 cm.

Now, let us draw the diagram to show how the resulting cuboid looks.

We can observe that when the two cubes are joined together end to end, the breadth and height of the resulting cuboid is 4 cm.

The length of the cuboid is the sum of the lengths of the sides of the two cubes.

Therefore, the length of the cuboid \[ = 4 + 4 = 8{\rm{ cm}}\].

Now, we will find the surface area of the resulting cuboid.

The total surface area of a cuboid is given by the formula \[2\left( {lb + bh + lh} \right)\], where \[l\] is the length, \[b\] is the breadth, and \[h\] is the height.

Substituting \[l = 8\] cm, \[b = 4\] cm, and \[h = 4\] cm in the formula, we get

Surface area of the resulting cuboid \[ = 2\left( {8 \times 4 + 4 \times 4 + 8 \times 4} \right){\rm{ c}}{{\rm{m}}^3}\]

Multiplying the terms in the parentheses, we get

Surface area of the resulting cuboid \[ = 2\left( {32 + 16 + 32} \right){\rm{ c}}{{\rm{m}}^3}\]

Adding the terms in the parentheses, we get

Surface area of the resulting cuboid \[ = 2\left( {80} \right){\rm{ c}}{{\rm{m}}^3}\]

Multiplying 2 by 80, we get

Surface area of the resulting cuboid \[ = 160{\rm{ c}}{{\rm{m}}^3}\]

**Therefore, the surface area of the resulting cuboid is 160 cubic centimetres.**

**Note:**We need to keep in mind that the words “surface area” refer to the total surface area, and not the curved/lateral surface area, unless specified. We might make a mistake by calculating the curved surface area instead of the total surface area using the formula \[2h\left( {l + b} \right)\].

We need to also understand that the \[64 {\rm{c}}{{\rm{m}}^3}\] is the volume of both the cube and not the volume of just one cube. If we take it as the volume of one cume then it will be wrong.

Recently Updated Pages

Mark and label the given geoinformation on the outline class 11 social science CBSE

When people say No pun intended what does that mea class 8 english CBSE

Name the states which share their boundary with Indias class 9 social science CBSE

Give an account of the Northern Plains of India class 9 social science CBSE

Change the following sentences into negative and interrogative class 10 english CBSE

Advantages and disadvantages of science

Trending doubts

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE

Difference Between Plant Cell and Animal Cell

Which are the Top 10 Largest Countries of the World?

10 examples of evaporation in daily life with explanations

Give 10 examples for herbs , shrubs , climbers , creepers

Write a letter to the principal requesting him to grant class 10 english CBSE

Change the following sentences into negative and interrogative class 10 english CBSE